Q1: Let $\mathcal{B} = (\mathbf{u}, \mathbf{v})$ be a basis of a subspace $U\subseteq \mathbb{R}^n$. What is the dimension of $U$?

A1: $2$

A2: $0$

A3: $1$

A4: $3$

A5: $4$

Q2: Let $n \geq 3$. Let $U \subseteq \mathbb{R}^n$ be a subspace. Which number can never be the dimension of $U$?

A1: $-1$

A2: $0$

A3: $1$

A4: $n-1$

A5: $n$

A6: $2$

Q3: Let $U = { \mathbf{x} \in \mathbb{R}^2 \mid \langle \mathbf{x} , \binom{2}{1} \rangle = 0}$. What is the dimension of $U$?

A1: $1$

A2: $0$

A3: $-1$

A4: $2$

A5: $\frac{1}{2}$